A Shape Theorem for Riemannian First-Passage Percolation

Riemannian first-passage percolation (FPP) is a continuum model, with a distance function arising from a random Riemannian metric in $\R^d$. Our main result is a shape theorem for this model, which says that large balls under this metric converge to a deterministic shape under rescaling. As a consequence, we show that smooth random Riemannian metrics are geodesically complete with probability one

Geodesics of Random Riemannian Metrics

We analyze the disordered Riemannian geometry resulting from random perturbations of the Euclidean metric. We focus on geodesics, the paths traced out by a particle traveling in this quenched random environment. By taking the point of the view of the particle, we show that the law of its observed environment is absolutely continuous with respect to the law of the random metric, and we provide an explicit form for its Radon-Nikodym derivative. We use this result to prove a "local Markov property" along an unbounded geodesic, demonstrating that it eventually encounters any type of geometric phenomenon. We also develop in this paper some general results on conditional Gaussian measures. Our Main Theorem states that a geodesic chosen with random initial conditions (chosen independently of the metric) is almost surely not minimizing. To demonstrate this, we show that a minimizing geodesic is guaranteed to eventually pass over a certain "bump surface," which locally has constant positive curvature. By using Jacobi fields, we show that this is sufficient to destabilize the minimizing property.Comment: 55 pages. Supplementary material at arXiv:1206.494

Linearity of cortical receptive fields measured with natural sounds

How do cortical neurons represent the acoustic environment? This question is often addressed by probing with simple stimuli such as clicks or tone pips. Such stimuli have the advantage of yielding easily interpreted answers, but have the disadvantage that they may fail to uncover complex or higher-order neuronal response properties. Here, we adopt an alternative approach, probing neuronal responses with complex acoustic stimuli, including animal vocalizations. We used in vivo whole-cell methods in the rat auditory cortex to record subthreshold membrane potential fluctuations elicited by these stimuli. Most neurons responded robustly and reliably to the complex stimuli in our ensemble. Using regularization techniques, we estimated the linear component, the spectrotemporal receptive field (STRF), of the transformation from the sound (as represented by its time-varying spectrogram) to the membrane potential of the neuron. We find that the STRF has a rich dynamical structure, including excitatory regions positioned in general accord with the prediction of the classical tuning curve. However, whereas the STRF successfully predicts the responses to some of the natural stimuli, it surprisingly fails completely to predict the responses to others; on average, only 11% of the response power could be predicted by the STRF. Therefore, most of the response of the neuron cannot be predicted by the linear component, although the response is deterministically related to the stimulus. Analysis of the systematic errors of the STRF model shows that this failure cannot be attributed to simple nonlinearities such as adaptation to mean intensity, rectification, or saturation. Rather, the highly nonlinear response properties of auditory cortical neurons must be attributable to nonlinear interactions between sound frequencies and time-varying properties of the neural encoder

Enhancement of Entanglement Percolation in Quantum Networks via Lattice Transformations

We study strategies for establishing long-distance entanglement in quantum networks. Specifically, we consider networks consisting of regular lattices of nodes, in which the nearest neighbors share a pure, but non-maximally entangled pair of qubits. We look for strategies that use local operations and classical communication. We compare the classical entanglement percolation protocol, in which every network connection is converted with a certain probability to a singlet, with protocols in which classical entanglement percolation is preceded by measurements designed to transform the lattice structure in a way that enhances entanglement percolation. We analyze five examples of such comparisons between protocols and point out certain rules and regularities in their performance as a function of degree of entanglement and choice of operations.Comment: 12 pages, 17 figures, revtex4. changes from v3: minor stylistic changes for journal reviewer, minor changes to figures for journal edito

Primary gas thermometry by means of laser-absorption spectroscopy: Determination of the Boltzmann constant

We report on a new optical implementation of primary gas thermometry based on laser absorption spectrometry in the near infrared. The method consists in retrieving the Doppler broadening from highly accurate observations of the line shape of the R(12) $\nu_{1} + 2 \nu_{2}^{\phantom{1}0} + \nu_{3}$ transition in CO$_{2}$ gas at thermodynamic equilibrium. Doppler width measurements as a function of gas temperature, ranging between the triple point of water and the gallium melting point, allowed for a spectroscopic determination of the Boltzmann constant with a relative accuracy of $\sim1.6\times10^{-4}$.Comment: Submitted to Physical Review Letter

Relationships between soil macroinvertebrates and nonnative feral pigs (Sus scrofa) in Hawaiian tropical montane wet forests

Abstract Nonnative feral pigs (Sus scrofa) are recognized throughout the New World as a highly significant introduced species in terms of ecosystem alteration. Similarly, nonnative soil macroinvertebrates (e.g. earthworms, ground beetles) invade and alter the structure and function of native habitats globally. However, the relationship between feral pigs and soil macroinvertebrates remains largely unknown. This study analyzed relationships between these taxa using nine sites located inside and outside of feral pig management units representing a * 25 year chronosequence of removal in tropical montane wet forests in Hawai‘i. Soil macroinvertebrates were sampled from plots categorized as: actively trampled by feral pigs, actively rooted by feral pigs, feral pigs present with no signs of recent activity, or feral pigs removed over time. In total, we found 13 families of primarily nonnative soil macroinvertebrates. Plots with active trampling correlated with lower total macroinvertebrate abundance, biomass, and family richness. Plots with active rooting were correlated with higher abundance of nonnative earthworms (Lumbricidae and Megascolicidae) and ground beetles (Carabidae). The abundance, biomass, and biodiversity of macroinvertebrates did not vary with time since feral pig removal. Collectively, these results indicate: (1) trampling by feral pigs negatively influences soil macroinvertebrates; (2) feral pigs either modify habitats while rooting thereby facilitating earthworm and ground beetle habitat use or selectively seek out target prey species of soil macroinvertebrates; and (3) removal of feral pigs has minimal impacts on soil macroinvertebrates over time. These results are important globally due to the broadly overlapping ranges of S. scrofa and nonnative macroinvertebrates

Thermophoresis of Brownian particles driven by coloured noise

The Brownian motion of microscopic particles is driven by the collisions with the molecules of the surrounding fluid. The noise associated with these collisions is not white, but coloured due, e.g., to the presence of hydrodynamic memory. The noise characteristic time scale is typically of the same order as the time over which the particle's kinetic energy is lost due to friction (inertial time scale). We demonstrate theoretically that, in the presence of a temperature gradient, the interplay between these two characteristic time scales can have measurable consequences on the particle long-time behaviour. Using homogenization theory, we analyse the infinitesimal generator of the stochastic differential equation describing the system in the limit where the two characteristic times are taken to zero; from this generator, we derive the thermophoretic transport coefficient, which, we find, can vary in both magnitude and sign, as observed in experiments. Furthermore, studying the long-term stationary particle distribution, we show that particles can accumulate towards the colder (positive thermophoresis) or the warmer (negative thermophoresis) regions depending on the dependence of their physical parameters and, in particular, their mobility on the temperature.Comment: 9 pages, 4 figure

Ιστορική και πολεοδομική εξέλιξη της πόλης του Βερολίνου - Συγκριτική μελέτη αναβάθμισης υποβαθμισμένων περιοχών σε Αθήνα και Βερολίνο

130 σ.Αντικείμενο της διπλωματικής εργασίας είναι η ιστορική αναδρομή και πολεοδομική εξέλιξη της πόλης του Βερολίνου από την ίδρυσή της μέχρι σήμερα, όπως και η σύγκριση δύο πρώην υποβαθμισμένων περιοχών που αναβαθμίστηκαν τις τελευταίες δύο δεκαετίες, σε Βερολίνο και Αθήνα αντίστοιχα. Η περιγραφή αυτή έχει ως σκοπό την παρουσίαση της σπουδαιότητας και του ρόλου του Βερολίνου δια μέσου των αιώνων, την επισήμανση των πολιτικών, νομοθετικών και πολεοδομικών γεγονότων και εξελίξεων που έπαιξαν σημαντικό ρόλο στην πορεία του, καθώς και τον εντοπισμό ομοιοτήτων και διαφορών από την ανάλυση της σύγκρισης των δύο περιοχών μελέτης. Η παρούσα διπλωματική εργασία αποτελείται από έξι κεφάλαια. Στο Κεφάλαιο 1 δίνονται γενικές πληροφορίες για το Βερολίνο, περιγράφοντας τη γεωγραφική θέση και έκταση, το κλίμα, τον πληθυσμό, τα δημογραφικά στοιχεία και την διοικητική διαίρεση της πόλης. Στο Κεφάλαιο 2 παρουσιάζεται η ιστορική αναδρομή του Βερολίνου από την ίδρυση του το 1237 μέχρι και σήμερα, επισημαίνοντας τα σημαντικότερα ιστορικά γεγονότα. Στο Κεφάλαιο 3 αναλύονται πολεοδομικά σχέδια (Σχέδια Χρήσης Γης), που έπαιξαν σημαντικό ρόλο στην εξέλιξη του Βερολίνου, ως προς τον σκοπό, το περιεχόμενο και τις επιπτώσεις τους, περιγράφοντας παράλληλα την πολιτική, νομοθετική και πολεοδομική εξέλιξη της πόλης. Στο Κεφάλαιο 4 εξετάζεται η αναβάθμιση της περιοχή μελέτης Warschauer Straße του Βερολίνου. Στο Κεφάλαιο 5 εξετάζεται η αναβάθμιση της περιοχής μελέτης του Γκαζιού της Αθήνας. Στο Κεφάλαιο 6 περιλαμβάνονται τα συμπεράσματα και τα αποτελέσματα της σύγκρισης των δύο περιοχών μελέτης.Subject of the thesis is the historical overview and urban development of the city of Berlin from its foundation until today, as well as the comparison of two formerly degraded areas that have been upgraded over the past two decades, in Berlin and Athens respectively. This description is intended to show the importance and role of Berlin through the ages, highlight political, legislative and planning events and developments that played an important role in its course, and identify similarities and differences from the comparison analysis of the two study areas. This thesis consists of six chapters. Chapter 1 contains general information about Berlin, describing the geographical location and area, climate, population, demographics and administrative division of the city. Chapter 2 presents the historical overview of Berlin from its founding in 1237 until today, highlighting the most important historical events. In Chapter 3 we continue with the analysis of the aim, the contents, and the impact of urban plans (Land Use Plans), which played an important role in the evolution of Berlin, while describing the political, legislative and urban development of the city. Chapter 4 examines the upgrade of the study area Warschauer Straße, Berlin. Chapter 5 examines the upgrade of the study area of Gazi, Athens. Chapter 6 gives the conclusions and results of the comparison of the two study areas.Βασίλειος Σ. Βλάχο

Thermal noise suppression: how much does it cost?

In order to stabilize the behavior of noisy systems, confining it around a desirable state, an effort is required to suppress the intrinsic noise. This noise suppression task entails a cost. For the important case of thermal noise in an overdamped system, we show that the minimum cost is achieved when the system control parameters are held constant: any additional deterministic or random modulation produces an increase of the cost. We discuss the implications of this phenomenon for those overdamped systems whose control parameters are intrinsically noisy, presenting a case study based on the example of a Brownian particle optically trapped in an oscillating potential.Comment: 6 page